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(2) The amount of the investment at the beginning of the third year was $4,326.40 Official Guide question Answer: D Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums! ### GMAT/MBA Expert Brent@GMATPrepNow GMAT Instructor Joined 08 Dec 2008 Posted: 10768 messages Followed by: 1213 members Thanked: 5156 times GMAT Score: 770 Fri Jul 28, 2017 5:44 am jjjinapinch wrote: A certain investment earned a fixed rate of 4 percent interest per year, compounded annually, for five years. The interest earned for the third year of the investment was how many dollars greater than that for the first year? (1) The amount of the investment at the beginning of the second year was$4,160.00
(2) The amount of the investment at the beginning of the third year was $4,326.40 Official Guide question Answer: D Target question: The interest earned for the third year of the investment was how many dollars greater than that for the first year? Given: A certain investment earned a fixed rate of 4 percent interest per year, compounded annually, for five years. So, we have: Let P = the initial investment After 1 year, the value of the investment = P(1.04) After 2 years, the value of the investment = P(1.04)^2 After 3 years, the value of the investment = P(1.04)^3 After 4 years, the value of the investment = P(1.04)^4 After 5 years, the value of the investment = P(1.04)^5 Statement 1: The amount of the investment at the beginning of the second year was$4,160.00
The value of the investment at the BEGINNING of the second year is the same as value of the investment at the END of the first year
So, we can write: P(1.04) = $4,160.00 Since we COULD solve this question for P, we COULD determine the value of the investment for each of the 5 years, which means we COULD answer the target question with certainty. As such, statement 1 is SUFFICIENT Statement 2: The amount of the investment at the beginning of the third year was$4,326.40
The value of the investment at the BEGINNING of the third year is the same as value of the investment at the END of the second year
So, we can write: P(1.04)^2 = $4,326.40 Since we COULD solve this question for P, we COULD determine the value of the investment for each of the 5 years, which means we COULD answer the target question with certainty. As such, statement 2 is SUFFICIENT Answer: D Cheers, Brent _________________ Brent Hanneson – Founder of GMATPrepNow.com Use our video course along with Check out the online reviews of our course Come see all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert Rich.C@EMPOWERgmat.com Elite Legendary Member Joined 23 Jun 2013 Posted: 8722 messages Followed by: 461 members Thanked: 2750 times GMAT Score: 800 Fri Jul 28, 2017 11:20 am Hi jjjinapinch, This is a great 'concept' question - meaning that if you recognize the concept(s) involved, you don't have to do much (if any) math to get to the correct answer. In this prompt, we're told that an investment earns a fixed 4% interest, compounded annually for 5 years. We're asked for the difference, in interest earnings, between the 3rd year and the 1st year. To start, we don't know the initial investment. However, since we're compounding the interest each year, then we know that the interest will be 4% of whatever total amount is already there. Thus, we have a constant 'multiplier' (1.04) that we'll just keep multiplying year-after-year. This means that if we know ANY dollar figure at any point in the 5 year history, then we can figure out ALL of the other values (using either division - to move backwards, or multiplication - to move forwards). 1) The amount of the investment at the beginning of the second year was$4,160.00

With this Fact, we can move 'backwards' and 'forwards' as described above and get the necessary information to answer the question.
Fact 1 is SUFFICIENT.

2) The amount of the investment at the beginning of the third year was \$4,326.40

Just as in Fact 1 (above), we can move 'backwards' and 'forwards' as described and get the necessary information to answer the question.
Fact 2 is SUFFICIENT.

GMAT assassins aren't born, they're made,
Rich

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Contact Rich at Rich.C@empowergmat.com

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